Related papers: Real trees in topology, geometry, and group theory
This survey is focused on the results related to topologies on the groups of transformations in ergodic theory, Borel, and Cantor dynamics. Various topological properties (density, connectedness, genericity) of these groups and their…
This is a survey. The main subject of this survey is the homotopical or homological nature of certain structures which appear in classical problems about groups, Lie rings and group rings. It is well known that the (generalized) dimension…
In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…
In this paper we analyse some questions concerning trees on $\kappa$, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in…
Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale…
We describe the topology of singular real algebraic curves in a smooth surface. We enumerate and bound in terms of the degree the number of topological types of singular algebraic curves in the real projective plane.
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
These lecture notes review the topological string theory and its applications to mathematics and physics. They expand on material presented at the Takagi Lectures of the Mathematical Society of Japan on 21 June 2008 at Department of…
We prove that given a fixed finite tree $P$, almost all trees contain $P$ as a subtree. Moreover, the inclusion can be made so that it induces an embedding of the corresponding (quantum) automorphism groups, thereby providing generic…
We present a careful approximation of the geodesics in trees of hyperbolic or relatively hyperbolic groups. As an application we prove a combination theorem for finite graphs of relatively hyperbolic groups, with both Farb's and Gromov's…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…